Equilibrium Of Forces Calculator

Work out equilibrium of forces instantly with clear inputs, formula shown and shareable results.

About Equilibrium Of Forces Calculator

A body is in equilibrium when the vector sum of forces is zero. Resolving each force into x and y components and adding them gives the resultant; the force needed to restore equilibrium is equal in size and opposite in direction. This is the closing side of the force polygon, and it is how a three-rope junction is solved.

Formulas

Component sums

Rx = sum F cos(theta); Ry = sum F sin(theta)

Equilibrant

F = sqrt(Rx^2 + Ry^2), acting 180 degrees from the resultant

Worked example

With the default values below, Equilibrium Of Forces Calculator returns Third Force Needed For Equilibrium of 70.752. Change any input above and every figure here is recalculated in your browser.

Inputs used

First forceminimum 0 N: 50 N
Direction of the first force: 30 deg
Second forceminimum 0 N: 70 N
Direction of the second force: 140 deg

Results

Third Force Needed For Equilibrium: 70.752 N
Direction It Must Act In: -81.61 deg
Resultant x Component: -10.322 N
Resultant y Component: 69.995 N

Step by step

1Values used
2Component sums
3Equilibrant
4Third Force Needed For Equilibrium= 70.752 N
5Direction It Must Act In= -81.61 deg
6Resultant x Component= -10.322 N
7Resultant y Component= 69.995 N

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is zero net force enough for equilibrium?

For a point, yes. An extended body also needs zero net moment, or it will rotate while its centre of mass stays put.

Which way do the angles run?

Anticlockwise from the positive x axis, the standard mathematical convention.